Download Market Clearing Price vs. Nominal Rigidities

Jacek Wallusch
The Poznań University of Economics
[email protected]
Macroeconomics and Competition: Market
Clearing Price vs. Nominal Rigidities
A chemist, physicist and economist are imprisoned. The chemist try to
fabricate an explosive, the physicist try to built a lever. The economist lays
on bed and thinks: “Consider that we have the keys”.
An old Polish joke
Keywords
Macroeconomics, competition, market clearing prices, nominal
rigidities
1. Introduction
An old saying teaches – learn the language of your enemy.
Translating the old wisdom into the specific language of the
contemporary economics, one should set up the model in the similar
way that the opponent does. The rival paradigms of the mainstream
economics often state that they speak the same language. The choice
of the paper’s language (obviously they chose the modern lingua
franca) is, however, where the similarities start and end. At the first
look the differences are even smaller than the differences between
Europe and America referred by Vincent Vega to Jules Wingfield.
Consider for example the New Classics and New Keynesians. Both
models use rational expectations, reductionism, Lucas-type
production function, there is even room for the optimising behaviour
in Keynesian theories. One small thing made the rivality exciting and
the models incomparable: an equilibrium price level.
The other old saying teaches that de gustibus non est
discutandum. Should we then talk about the assumptions or at least
about the reasons why a theorist set up her/his model in a particular
302
way? Naive intuition prompts to answer positively, because the
empirical works may provide some facts about the behaviour of the
agents. Nobody would trust the econometricians, however, in the
post-post-modern era. Is there any link between probability, truth
and econometrics 1? Many generations of theorists following Keynes
linked econometrics to black magic, and many generations will do
exactly the same. Moreover, many empiricists are of the same
opinion. Economics is thus an art of convincing the audience that the
structural assumptions hold and that they describe the real world.
Teaching history of economic thought, macroeconomics and
applying econometrics, market clearing price becomes the most
important assumption that must be explained.
Focusing on the market clearing price, lecturer is able to
connect micro and macro level. A standard approach leave the gap
between microeconomics and macroeconomics unbridged. Students
usually connect employment with the effective demand driven by the
investment level. This is probably the biggest puzzle why they are
unable to analyse the labour market using the basic microeconomics.
They start to think after a simple question: would you check out the
level of investment before entering the labour market, or would you
rather check out the real wage the firm would offer you? Perhaps the
biggest challenge for the lecturer is to show that the contemporary
macroeconomics is built on the microfoundations, though the
foundations are completely different. Even Keynes used a well
specified microeconomics presenting the liquidity preference and the
theory of effective demand. Thus, the aim of this paper is
straightforward: using some simple simulations I show the links
between microeconomics and macroeconomics. The paper presents
five easy pieces conducted in MS Excel. The exercises focus on
various approaches to the labour market analysis (1 and 3),
effectiveness of the monetary policy under different expectation
schemes (2), sticky price and real demand (4), and the meaning of
market clearing price (5). In almost all cases one innocent coefficient
is responsible for the huge differences between both paradigms.
1
Hugo Kuezenkamp knows the answer (2000). His book, however,
is not studied with the sufficient admiration, especially by the Polish
scientists.
303
2. Exercises
This section presents five basic exercises, which should help the
students to recognise the difference between paradigms. All
exercises are prepared in the MS Excel, in the initial period t0 all
indices = 100. The value of coefficients used in the exercises are
enlisted in the tables, though they may (or even should) be freely set
by the students. In two cases a stochastic term is added to the money
supply to visualise the effects of uncertainty under REH2.
Additionally, students should change the deterministic component of
the money supply. It would be especially helpful if the lecturer deals
with the question why is Keynesian economics sometimes
considered as explaining better the effects of decreasing demand.
The Excel file is available on my website:
www.wallusch-datenbank.de
(see Research/Publications).
Exercise 1. Keynes and the Labour Market
E.1.1. Aim
For some Keynesians (Okun 1981) the rigid nominal wage is the
most important element of the General Theory. This exercise shows:
1. The influence of the imperfect nominal wage elasticity on the
labour market;
2. The influence of the money illusion on the labour market.
E.1.2. Setup
Let the price level and nominal wage be as follows:
(1)
pt = pt −1 (α + β∆mt )
2
The stochastic term, generated using the MS Excel, satisfies the
standard properties, is normally distributed with zero-mean and a
finite variance.
304
wtn = wtn−1 [γ + (1 − γ )∆mt ], γ ∈ (0,1) .
The values of coefficients, assuming that p follows the quantity
theory, while the elasticity of nominal wages in respect to changes in
the money supply is imperfect, are presented in table 1.
(2)
Table 1. Coefficients’ value in Exercise 1.
coefficients:
α
β
γ
value:
0
1
0.75
The sum of coefficients in Eq. (1) must be equal to unity, so it form
might be the same like Eq. (2). The presented version of Eq. (1),
however, helps to understand the difference between optimal and
rigid price level. Labour supply is approximated by a function:
(3)
l tS = ltS−1 ⋅ ∆wtn ,
while the demand for labour is:
−1
 wn 
ltD = ltD−1 ⋅  ∆ t  .
 pt 
Since the labour supply is driven by changes in the nominal wage,
the workers suffer money illusion.
(4)
E.1.3. Summary
The figure visualises the difference between demand and supply in
the labour market. However, the crucial point of this exercise is to
show that the combination of the optimal price and sticky wage will
produce an increasing demand for labour caused by changes in
money supply (see demand for labour in the table, row 9). I usually
set the γ-coefficient to be equal to 0.51, but some interesting results
might be obtained after changing it to 0.5.
Exercise 2. Effectiveness of the Monetary Policy under
Adaptative and Rational Expectations (.xls-sheet: REH vs. AEH).
E.2.1. The Aim
305
A conventional wisdom says that a systematic monetary policy is
ineffective in the monetaristic models. Rational expectations (REH)
are often mistakenly interpreted as a perfect foresight. Hence, the
aim of this exercise is twofold:
1. Using the deterministic money supply scheme the exercise shows
that only REH ensures ineffectiveness of the systematic monetary
policy;
2. Using a simple stochastic money supply scheme the exercise
shows that even after imposing REH on the agents’ behaviour money
is not neutral.
E.2.2. Setup
Real output is described by a modified Lucas-type function:
(5)
yt = yt −1 + β [ pt − Et ( pt )] .
Price level follows the quantity theory of money:
(6)
pt = pt −1∆mt .
Consider first that the monetary authority controls entirely the
money supply. Let the adaptative scheme follows the two-period
weighting average:
(7)
EtAEH ( pt ) = γpt −1 + (1 − γ ) pt −2 , γ ∈ (0,1) .
Now, dropping down the assumption about the deterministic money
supply scheme, a stochastic term µ satisfying the standard properties:
(8)
µt = N (0, σ µ2 ) ,
is added. Obviously, µ might be generated using the MS Excel – in
this case I assumed that the variance σ µ2 = 1. Since the expected
value of the stochastic term µ is equal to zero, the output function
becomes:
(5a)
yt = yt −1 + [ pt − Et ( pt )] + µ t .
E.2.3. Summary
Although the actual price level follows the quantity theory, there is a
fundamental difference between the values of the REH- and AEHbased output functions. The upper panel depicts the various results.
306
Changes in money supply do not produce any changes in output
under REH. Hence, the first aim is obtained.
The difference between the values of the REH- and AEHbased output functions assuming a deterministic money supply
scheme is presented in the second figure. Here, even after imposing
rationality on the agents’ prediction, changes in money supply
produce changes in real output. Those changes do not depend,
however, on the systematic component in money supply.
Exercise 3. Labour Market: NCE vs. NKE (.xls-sheet: labour
market NCE vs. NKE).
E.3.1. The Aim
The nominal wages are rigid while prices are driven by the quantity
theory. According to Fischer (1991), the long-run commitments
might influence the nominal wages. In some aspects this Exercise is
similar to the Exercise 1, but a new classical model is added. Again,
the aim is twofold:
1. To show, using both money supply schemes, the difference
between optimising and suboptimising behaviour;
2. To show that the unexpected changes in money supply will
produce changes in employment under REH and optimising
behaviour.
Exercise 3. requires an additional comment. Analysing the
labour market students usually omit the microeconomic rationality of
agents and explain both demand and supply via investment level –
this is the situation I mentioned in the opening section. The exercise
should help the students to better recognise the link between microand macroeconomics.
E.3.2. Setup
Consider a model:
−1
(9)
(10)
 wn 
lt = lt −1 ⋅  ∆ t 
 pt 
pt = pt −1 (α + β∆mt )
307
wtn = wtn−1 (γ + δ∆mt ) ,
where: l – employment, p – price level, wn – nominal wage. Since the
price level follows the quantity theory, the coefficients in Eq. (10)
are α = 0, β = 1 . The values of the coefficients in Eq. (E.3) differ
subject to the paradigm and are presented in table 2.
(11)
Table 2. Coefficients in the Nominal Wage Equation.
Coefficient
γ
δ
NCE
0
1
NKE
1
0
E.3.3. Summary
Since the wages are rigid, while the prices change along with the
money supply, the increasing money supply produces a decrease in
real wages and an increase of the demand for labour. Hence, the
employment increases as well. On the other hand, if both prices and
wages are set at their optimal value the money is neutral. Upper
figure depicts both results.
Using the stochastic money supply scheme, the effects of
monetary changes under optimal behaviour are different. Again, the
real variable deviates from its initial value. This situation is
presented by the second figure.
Exercise 4. Real Demand and Rigidities (.xls-sheet: same title).
E.4.1. The Aim
The aim of this exercise is to learn the effects of sticky prices and
monetary changes. As stressed before, business fluctuations are
usually connected to the procyclical changes in interest rate and
investment. Increasing money supply lowers the nominal interest
rate and hence the marginal efficiency of capital increases. A
simplest way, however, is to show how the changes in money supply
affect real the effective demand.
308
E.4.2. Setup
Let the price equation be as follows:
(12)
pt = pt −1 [β + (1 − β )∆mt ] .
Obviously, for the Classics b is equal to 0, while for the Keynesians
(13)
β ∈ (0,1] .
The real demand y D is simply a combination of nominal supply and
the price level:
m
(14)
ytD = t .
pt
E.4.3. Summary
The consequences of monetary changes in a sticky prices economy is
one of the essential questions that Keynesian economics asks. The
straightforward interpretation should focus on the changes in real
demand, which varies along with the changes in money supply. This
is why monetary expansion (contraction) causes an increase
(decrease) in real output or employment.
Exercise 5. New Keynesians and the Market Clearing Price (.xlssheet: Near Rationality and MCP).
E.5.1. The Aim
Unlike the Post-Keynesians, New Keynesians employ the concept of
market clearing price. Their interpretation of the optimal price,
however, differs slightly from the one used by the Classics. The aim
of this exercise is to compare the New Keynesian and Classical
market clearing price.
E.5.2. Set-up
Following Akerlof and Yellen (1991), a price set by the optimising
firms is as follows:
θ
(15)
pt = pt −1 (1 + ∆mt ) ,
where:
309
(16)
θ=
(1 − α ) α
≤ 1.
β (η α − η + 1) + (1 − β )((1 − α ) α )
Here, the α is elasticity of output with respect to labour input, η is
elasticity of demand, and β is a fraction of non-maximising firms.
Money supply as well as all three parameters (α, η, β) might be
changed. Akerlof and Yellen proposed three values for α and β:
0.25, 0.5, 0.75, and five values of η: 1.5, 3, 5, 20, 100. The optimal
price level, according to the quantity theory, is the same as in
previous exercises.
E.5.3. Summary
Akerlof and Yellen used a price function that differs from the one
based on the quantity theory. The price set by the optimisers depends
not solely on the changes in money supply, but also on the fraction
of non-maximising firms. Along with an increase in the β-coefficient
the difference between the quantity theory-based optimal price and
the optimal price defined by Akerlof and Yellen becomes larger.
Thus, the price referred by the Authors to as ‘optimal’ is in fact not
optimal in the classical sense.
3. Summary
Contemporary mainstream macroeconomics seems to be very
complicated. After removing the sophisticated mathematical
constructions, however, the ideas are pretty simple. The differences
between Classics and Keynesians concern one small assumption:
pricing mechanism. The rest is irrelevant. No wonder that there is no
consensus among the economists. Teaching history of economic
thought, or more generally economic theory, a lecturer has to focus
on the rigidities and its consequences for the economic policy. The
aim of the above presented exercises was twofold. Firstly, they show
why there is no room for an active demand controlling-policy if the
perfect price elasticity is assumed. Secondly, they show why the
empirical investigation cannot unanimously decide which strategy is
the proper one. If the empiricist considers that the changes in money
supply are partly stochastic, the results might confirm both
310
strategies3. Everything originates in the assumptions. Whether the
economists have the keys – it remains an open question, while the
answers must be treated with the necessary caution.
4. Recommended reading
New Classical and New Keynesian models are described in Bludnik,
Szulc, and Wallusch (2005). The methodological problems are
presented by, among others, Kuezenkamp (2000) and Mayer (1996).
Okun (1991) and Mankiw and Romer (1991) provide an interesting
guide to the Keynesian economics of the 1970s and 1980s. Some
papers and books written by Belka and Wojtyna (e.g. 1993, Belka
1986) during their early academic career are of the primary
importance for the Polish-speaking students. More recently Wojtyna
(2000) described the evolution of the Keynesian economics.
ACKNOWLEDGEMENTS
I would like to thank Agata Godlewska-Kliber, Julia Gwizdała, and
Grzegorz Wlekły for their patience, comments on the early draft of
this paper, and help to be a better (what does not necessary mean that
I am not the worst) lecturer.
References:
1.
2.
3.
Akerlof, G. A., and J. L. Yellen (1991), A near-Rational
Model of the Business Cycle, with Wage and Price Inertia,
in: Mankiw, N. G. and D. Romer (eds.), New Keynesian
Economics, Vol. 1, Imperfect Competition and Sticky
Prices, MIT Press.
Belka, M. (1986), Doktryna ekonomiczno – społeczna
Miltona Friedmana, PWN: Warszawa.
Belka, M. and A. Wojtyna eds. (1993), Współczesny
keynesizm, in: Studia i Materiały PAN INE 42, Poltext:
Warszawa.
3
Thomas Sargent analysed this situation in the mid 1970s. Some
useful tool is provided by Cochrane (1998).
311
4.
Bludnik, I., Szulc, R., Wallusch, J. (2005), Materiały
pomocnicze do ćwiczeń z Historii Myśli Ekonomicznej, ed.
by M. Ratajczak and Z. Romanow, Wydawnictwo AE w
Poznaniu.
5. Cochrane, J. H. (1998), What Do the VAR Mean?
Measuring the Output Effect of Monetary Policy, Journal of
Monetary Economics 41, 277-300.
6. Fischer, S. (1991), Long-Term Contracts, Rational
Expectations, and the Optimal Money Supply Rule, in:
Mankiw, N. G. and D. Romer (eds.), New Keynesian
Economics, Vol. 1, Imperfect Competition and Sticky
Prices, MIT Press, 215-231.
7. Keuzenkamp, H. (2000), Probability, Econometrics and
Truth. The Methodology of Econometrics, Cambridge
University Press.
8. Mankiw, N. G. and D. Romer (1991), Introduction, in:
Mankiw, N. G. and D. Romer (eds.), New Keynesian
Economics, Vol. 1, Imperfect Competition and Sticky
Prices, MIT Press.
9. Mayer, T. (1996), Prawda kontra precyzja w ekonomii, WN
PWN: Warszawa.
10. Okun, A. M. (1991), Ceny i ilości. Analiza
makroekonomiczna, WN PWN: Warszawa.
11. Wojtyna, A. (2000), Ewolucja keynesizmu a główne nurty
ekonomii, WN PWN: Warszawa.
312